Question

If secx = root 2 and 3pi/2 < x < 2pi find the value of 1+tanx+cosecx/1+cotx-cosecx...........very urgent pleassssss

Answer 1

Answer:

ATQ:

3π/2<x<2π

that means X lies in the fourth quadrant .

In that quadrant remember all values of sin,tan and cosec is negative.

secx=√2

x= sec-¹(√2)

x=π/4;

but π/4 lies in the 1st quadrant but 2π-π/4 will lie in the 4th quadrant therefore

tan(2π-π/4)= -1

cosec(2π-π/4)= -√2

cot(2π-π/4)= -1

therefore

1+tanx+cosecx/1+cotx-cosecx=1-1-√2/1-1+√2= -√2/√2= -1

therefore ans = -1